The marginalist revolution and the development of the neoclassical paradigm: models and methods

Carl Menger's (1871) contribution was more clear, but less formal. Although he did not name it explicitly, he introduced the concept of diminishing marginal utility in general discussion. He just referred to the decreasing "importance of the satisfaction of needs" and used numerical examples (Menger, 1871: p.127) to illustrate the idea. [Note: the term "marginal utility", Grenznutzen, was only introduced by Friedrich von Wieser (1889); in his work, Menger uses the term "utility" in the same misleading sense Adam Smith did, i.e. in terms of objective "use-value"]. As a result, Menger comes to the Marginalist conclusion:

"Value is therefore nothing inherent in goods, no property of them, but merely the importance we atribute to the satisfaction of our needs, that is, to our lives and well-being, and in consequence carry over to economic goods as the exclusive causes of the satisfaction of our needs." (Menger, 1871: p.116)

Menger did not bother to derive a demand function, but his discussion of exchange, in many ways, supersedes that of Jevons. In particular, he defined prices as "only incidental manifestations of [exchange], symptoms of an economic equilibrium between the economies of individuals." (Menger, 1871: p.191). Prices, then, are formed by market processes of exchange and the nature of the process can vary depending on a variety of factors, notably in the degree of competitiveness. In his famous Chapter 5, Menger outlines the process of price-formation from a bargaining process between two individuals, under monopoly, duopoly and, finally, competition. Although he was not consistent (e.g. at one time recognizing the indeterminacy of prices in bilateral exchange, and then retreating from this elsewhere), Menger's analysis of the market process was highly suggestive and marked the approach of the Austrian School in years to come.

Two other points insisted upon by Menger are worth mentioning. Firstly, his distinction between economic goods and non-economic (i.e. free) goods was given central importance (Menger, 1871: p.94-109). He underlined the fact that one cannot assume that goods have prices; whether a good is free or not is a result of the final equilibrium configuration and thus is endogenous to the problem. Secondly, Menger (1871: p.149-74) outlined the important theory of imputation. As only utility can confer value, then the value of factors of production ("goods of higher order") which have no utility in and of themselves must be determined by the prices of outputs ("goods of lower order"). This is the heart of the Neoclassical treatment of production as "indirect exchange".

The contribution of Léon Walras (1874) outshines both Jevons, Menger and all other predecessors in clarity, rigor and insight. It is in Walras where we find the most careful, complete and visionary statements of the Marginalist Revolution. As Schumpeter expressed it, with characteristic lack of restraint:

"Walras is in my opinion the greatest of all economists. His system of economic equilibrium, uniting, as it does, the quality of a "revolutionary" creativeness with the quality of classic synthesis, is the only work by an economist that will stand comparison with the achievements of theoretical physics. Compared with it, most of the theoretical writings of that period - and beyond - however valuable in themselves and however original subjectively, look like boats beside a liner, like inadequate attempts to catch some particular aspects of Walrasian truth." (J. A. Schumpeter, 1954: p.827)

The details of Walras's general equilibrium system are given elsewhere,, so we shall note only a few of his contributions here. Walras adopted the notion of marginal utility and the scarcity theory of value from his father, Auguste  Walras (1831). However, Auguste Walras did not manage to connect the two concepts. Already in his early work, we find the young Léon Walras following his father in claiming that the value of goods depends on both utility and rarity ("rareté"). Walras then was holding on to an objective definition of rarity, defining a good as rare if "it is offered to general demand in a limited quantity" (Walras, 1860: p.8).

It was only in an 1873 article preceeding his Elements (1874) that Léon Walras took the leap and made the connection by noting that "rareté is personal or subjective" (Walras, 1874: p.146). Walras used the term rareté for "marginal utility". At least for the case of bilateral trade, this is an extremely fortuituous use of language -- for what does marginal utility of a particular good represent other the intensity with which that good is needed and thus the degree to which its absence is felt? If my marginal utility for eggs is greater than yours, then eggs are perceived by me as being more scarce than they are perceived by you.

Walras's use of the term rareté keeps the fundamental Neoclassical idea of subjective scarcity at all times in the forefront of our minds and does not let it slip out of sight. However, moving beyond exchange between two parties, the connection becomes more tenuous: scarcity is a market-wide phenomenon; marginal utility is an individual phenomenon, and thus his use of the term rareté for marginal utility may be confusing in the case of economy-wide exchange.

The rest of Walras's work is sheer brilliance. Recognizing the multi-good nature of exchange, all of Walras's analysis proceeds with multiple markets. No oversimplifying ceteris paribus assumptions are made. Alone among the early Marginalists, Walras provided a proper derivation of the demand curve from utility functions via the use of household budgets (Walras, 1874: Ch. 8, 11.). If anything is demanded, something else must be offered in exchange; consequently the aggregate value of what is offered must equal the aggregate value of what is demanded. As a result, for any bundle of goods demanded x = [x₁, x₂, .., x_n] and for a given set of endowments e = [e₁, e₂, .., e_n], it must be that:

p₁x₁ + p₂x₂ + ... + p_nx_n = p₁e₁ + p₂e₂ + ... + p_ne_n

Walras's recognized that the need for a numeraire good enabled him to fix one price, e.g. p₁ = 1. In this case:

x₁ + p₂x₂ + ... + p_nx_n = e₁ + p₂e₂ + ... + p_ne_n

where p₂, p₃, etc. are the prices of goods x₂, x₃, etc. in terms of the price of good x₁. Now, Walras used an additively separable utility function so that the utility of a bundle x can be written as:

U(x) = u₁(x₁) + u₂(x₂) + ... + u_n(x_n)

where u_i(x_i) is the utility from good x_i. Substituting the budget constraint into the first of these separate utilities:

U(x) = u₁(e₁ + p₂e₂ + ... + p_ne_n - p₂x₂ - ... - p_nx_n) + u₂(x₂) + ... + u_n(x_n)

which, upon maximization, yields for any good x_i the following first order condition:

U/ x_i = -( u₁/ x₁)·p₂ + u₂/ x₂ = 0

or letting MU_i = u_i/ x_i, then we obtain the result:

MU₁ = MU_i/p_i

for every i = 1, .., n. This is Gossen's Second Law once again.

As we have n goods, we have n-1 such equations. The addition of the aggregate budget constraint equation implies we have a total of n equations. What about unknowns? As prices are given, then all we have to do is determine the amounts demanded/supplied by agents, x₁, .., x_n. With an equal number of equations and unknowns, we are there and can express our resulting individual demand functions as:

x_i = x_i(p₁, .., p_n)

for i = 1, .., n. He aggregates these into market demand/supply functions by horizontal summation over households. Equilibrium is achieved when market demand is equal to market supply in each market. Walras goes on to his unique discussion of the stability of equilibrium via his tatonnement price adjustment process, to which we refer elsewhere. Finally, Walras goes beyond the other pioneering Marginalists in proceeding, in later chapters,  to incorporate production, capital and money into his general equilibrium model in a complete and consistent manner.

[Note: William Jaffé (1976) has noted that "instead of climbing up from marginal utility to the level of his general equilibrium system, Walras actually climbed down from that level to marginal utility". This seems evident from reading Walras. As such, at least in Walras's case, one might be tempted to play down the influence of the French utility-cum-scarcity tradition in favor of the other French tradition of "grand systems" of general equilibrium (cf. Cantillon, 1755; Quesnay, 1759, Turgot, 1766; Isnard, 1781).]

The works of  Jevons, Menger and Walras were met with different reactions. Jevons's Theory received various notices and reviews, some of them sympathetic, many of them hostile (Alfred Marshall's (1872) review was noticeably lukewarm). At any rate, one could not fail to notice it. Even textbooks written in the Classical tradition, such as John E. Cairnes (1874) and Henry Sidgwick (1883), were forced to make some note or other about Jevons's new theory.

In contrast, a complete silence surrounded Léon Walras's Elements -- the only notice of the existence of this book were Walras's own follow-up publications, most of them also duly ignored. Walras became aware of Jevons's existence in 1874 and gracefully acknowledged his priority. They took to each other immediately and made a joint effort to spread the word. Something akin to a division of labor ensued: Jevons went off digging up illustrious predecessors in order to enhance the pedigree of the new doctrine while Walras endeavored to establish communication with virtually every important economist of the day. Jevons's task proved to be more rewarding: in his efforts, he helped unearth Cantillon, Cournot and Gossen out of their obscurity. In contrast, Walras just found shut doors and impatient listeners. Only a handful of the economists he contacted responded positively to the new ideas. In frustration, he turned to contemporary mathematicians, only to be dismissed once again.

Menger, who did not exactly cooperate with the Jevons-Walras efforts, went on his own crusade. His 1883 Investigations provoked prominent German-speaking economists such as Gustav Schmoller into a bruising debate on methodology. This Methodenstreit enhanced general awareness of Menger's new theory, but it also bogged him down. In the end, it was somewhat self-defeating: although his fame and reputation were greatly increased in  Austria, the entire university system in Germany itself was closed to him and his followers.

The Marginalist Revolution really began only to take off in the 1880s with the publication of the works of a younger generation which had begun to read up on their works. The wide dissemination of the work of two close disciples of Menger, Friedrich von Wieser (1884, 1889) and Eugen von Böhm-Bawerk (1886, 1889), gave the theories of the Austrian School wider attention.

The mathematical tone of Jevons's and Walras's own works attracted a slew of technically-gifted young economists throughout the world. Among these we can count the Englishmen Francis Ysidro Edgeworth (1881) and Philip H. Wicksteed (1888), the Austrians Rudolf Auspitz and Richard Lieben (1889), and, a little later, the American Irving Fisher (1892) and the Swede Knut Wicksell (1893).

The trickle of the 1880s turned into the flood of the 1890s, particularly after the joint discovery of the marginal productivity theory of distribution by the American economist John Bates Clark (1890, 1899), Knut Wicksell (1893), Philip H.Wicksteed (1894) and Enrico Barone (1895). The Marginalist Revolution then went into high gear with the publications of  Maffeo Pantaleoni (1889), Vilfredo Pareto (1892, 1896-7, 1906), Knut Wicksell (1898, 1901, 1906) and Giovanni B. Antonelli (1886). Details on the consolidation of the Neoclassical theory of value by these economists are found elsewhere.

Nonetheless, the most significant event of the 1890s was the publication of Alfred Marshall's Principles of Economics (1890). This is notable not so much for the research or insights which it generated, but rather because it was the first really successful Neoclassical textbook. It was through Marshall that the Marginalist Revolution became palatable to contemporary economists -- Marshall's extremely conciliatory attitude towards the displaced Classical School was the sugar that permitted it be swallowed by fellow academics. Through its wide adoption as a university textbook, Neoclassical theory was delivered to a wider public. The infamous "demand-and-supply" diagram with the reversed axes that has since become the standard staple of economics textbooks was a centrepiece of Marshall's book. In other countries, the works of  Knut Wicksell, Maffeo Pantaleoni, Etienne Antonelli and others gained wide textbook usage, but in English-speaking countries, despite several efforts at displacement (e.g. by Wicksteed (1910)), the successive editions of Alfred Marshall's Principles remained the dominant text at least until the 1930s.

[Note: Alfred Marshall irritatingly continued to insist time and time again that he had basically formed most of his ideas before he had read Jevons's 1871 volume (cf. Marshall notes and letters in Pigou, 1925), and thus that he should be counted as one of the original "revolutionaries". He pointed to two 1879 articles printed for "private circulation" as evidence of his habit of coming up with new ideas, but not rushing them to publication. However, most historians of economics have concluded that Marshall claims to originality have no basis. It is quite apparent that Marshall did derive most of his own theory after reading Jevons. For further notes on Marshall and his role in the Marginalist Revolution, see Whitaker (1975), Maloney (1985) and Mirowski (1990). In contrast, we should note that John Bates Clark (1885) did arrive at his utility-based theory of price while quite ignorant of the work of Jevons, Menger and Walras -- and thus Clark, but not Marshall, should be given high marks for originality.]

Although sharing the same underlying Neoclassical theory of value, the different emphasis, approaches and methods of the various pioneering Marginalists on details such as production, money, capital, dynamics, etc. led to the segmentation of the Neoclassical school into various largely independent "schools of thought", rather than consolidation into a "monolothic" Neoclassical edifice. The Cambridge Neoclassicals followed Marshall's approach, the Austrian School followed Menger Böhm-Bawerk and Wieser, while the Chicago School followed a combination of both Marshall and the Austrians. Naturally, the Stockholm School followed Wicksell, and and one can even divide the Lausanne School further intosubsequently distinct Walrasian and Paretian traditions. 

However, this segmentation should be treated with caution. Some Neoclassical economists, such as Jevons, Wicksteed and Fisher failed to belong to or develop behind them any clear "school of thought". Furthermore, there was a good degree of cross-pollination among schools -- for instance, the influence of the Austrians on the Swedes (and vice-versa) is well-documented. Finally, there were occasions when several economists attempted to hammer the disparate contributions of the different schools of thought together into a single, all-encompassing "Neoclassical" theory. Such efforts are discernable, for instance, in the 1930s, 1960s and the 1980s, although not always successful.

Finally, we should note that the "Marginalist Revolution" had severer growing pains than this brief account indicates. Initiated in 1871-4, it only began to be noticed in the 1880s and by the late 1890s it was already running out of steam. In the early part of the twentieth century, the Marginalist Revolution was, in fact, retreating on many fronts. The great splash in the 1880s excited both support and opposition and, as a result, it advanced quickly and generated great professional debates that helped it become better known. However, a mere two decades later, we begin to notice that Neoclassicism seemed more and more to have become a peripheral "fringe" movement in the economics profession as a whole.

The reasoning for the Neoclassical retreat in the 1900s is largely because, to many contemporaries, it seemed to be descending into "quackery". Originally, the Neoclassicals had promised that their approach would provide a more sound, "scientific" explanation of economic phenomona than the alternative Classical, Institutional or Historical approaches. However, its Achilles' heel was the very notion of "marginal utility". Marginal utility, let us be frank, is hardly a scientific concept: unobservable, unmeasurable and untestable, marginal utility is a notion with very dubious scientific standing.  As Stigler notes, "Had specific tests been made of the implications of theories, the unfruitfulness of the ruling utility theory as a source of hypotheses in demand would soon have become apparent" (G.J. Stigler, 1950).

However, it was given the benefit of the doubt in the 1880s by contemporary economists as a tentative hypothesis that was helpful to economic analysis, but which, hopefully, could be dispensed with later. But it quickly became apparent that rather than being a small part of the Neoclassical paradigm, it was increasingly becoming the "all" of Neoclassicism. Everything was beginning to be reduced with almost religious devotion into this nebulous hedonistic concept and thus seemed less and less "scientific".  As Henry L. Moore, an early disciple of Walras, wrote:

"In the closing quarter of the last century, great hopes were entertained by economists with regard to the capacity of economics to be made "an exact science". According to the view of the foremost theorists, the development of the doctrine of utility and value had laid the foundation of scientific economics in exact concepts, and it would soon be possible to erect upon the new foundation a firm structure of interrelated parts which, in definiteness and cogency, would be suggestive of the severe beauty of the mathematico-physical sciences. But this expectation has not been realized." (H.L.  Moore, 1914: p.84-85)

The indulgence contemporary economists had granted to the Neoclassical marginal utility hypothesis in the 1880s was largely withdrawn by the 1900s. In contemporary eyes, Neoclassicals were "quacks": they had promised a "scientific" approach and instead yielded up a "religious" approach to economics. Contemporary economists echoed with approval the merciless ridicule that Thorstein Veblen heaped upon Neoclassical quackery. As Jacob Viner was to lament in 1925:

"In the scientific periodicals, however, in contrast with the standard treatises, sympathetic expositions of the utility theory of value have become somewhat rare. In their stead are found an unintermittent series of slashing criticisms of the utility economics." (J. Viner, 1925).

By and large, economists throughout the world withdrew from Neoclassicism and moved back into what seemed like "more serious science": i.e. the empirical approach of the Institutional and Historical schools. There were a few isolated exceptions: at Cambridge, Chicago and Vienna, Neoclassical dominance was maintained through the early part of the 20th Century. At the University of Cambridge (UK), Neoclassicism survived because it was a pretty self-contained place anyway -- "everything is in Marshall", they believed (although things changed considerably after Sraffa's 1926 attack, and particularly, after Keynes's 1936 General Theory). The University of Chicago survived as a Neoclassical bastion in good part because of it was composed of a few strong personalities -- esp. Frank Knight, Jacob Viner, Henry  Schultz -- who were gripped by siege mentality (witness their extensive journal forays in defense of Neoclassical methodology). The third exception was the University of Vienna -- which was also energized by a siege mentality and wilful personalities. However, the Austrian Neoclassicals held on there only until the end of the First World War, when they were finally dispersed.  Consequently, for nearly thirty years, Neoclassical economics was effectively moribund, being slowly pushed forward by a handful of economists hidden away at Cambridge, Chicago and a few other scattered places .  

This state of affairs changed drastically during the 1930s, when the Neoclassicals began rolling back in. The most significant institutional event was the "reconquest" of the London School of Economics by Lionel Robbins in the early 1930s -- and a parallel "half-conquest" of Harvard by Joseph Schumpeter and Wassily Leontief. The formation of the Cowles Commission and the Econometric Society put the Neoclassicals back in touch with each other and the research energy that emerged was remarkable. Paradoxically, Hitler's armies contributed to this process:  by expelling many economists from Central Europe, they effectively forced them to reassemble together at places like the LSE, Cowles and other institutions.

But it was the theoretical achievements of the 1930s on the part of a handful of a few young technically-minded economists that saved Neoclassical economics. The Hicks-Allen "ordinalist" revolution and Paul Samuelson's "revealed preference" approach helped remove much of the quackery that stained utility theory. It gained an empirical plausibility which had been missing before -- or at least, in the words of one contemporary economist, it was no longer "repugnant to our logic to suppose that [experiments] can be made" (Ricci, 1933: p.15). Welfare economics, firstly via A.C.  Pigou and then through the hands of Harold Hotelling, Oskar Lange, Maurice Allais and the L.S.E. economists (John Hicks, Abba Lerner, etc.), demonstrated that there was still something quite useful in the hypothesis.  At any rate, Cassel's resurrection of the Walrasian general equilibrium system, the consolidation of the Neoclassical theory of production, the empirical efforts of Shultz and Douglas, and even Hayek's foray into macroeconomics were all done on the basis of demand functions -- without utility -- thereby demonstrating that there remained huge swathes of Neoclassical theory were not too reliant on that dubious hedonistic concept.  All these theoretical developments helped lend "scientific" teeth to Neoclassicism that were previously missing.

The rest of the story is too well-known. After the fervor of the 1930s -- the "Paretian revival" as we have chosen to call it -- Neoclassical theory managed to displace virtually all other theories and approaches from economics. Thus, the "Marginalist Revolution" was not something that just happened in the 1870s, but, in fact, it took at least six decades to entrench itself. Cheekily, some historians have preferred to call the early period merely the "Marginalist Insurrection".

Some would argue it took even longer to attain its monopoly over the economics profession. At least four other important paradigmatic challenges were hatched during the 20th Century which slowed down the Neoclassical ascendancy or at least prevented its complete dominance:  Monopolistic Competition, the Keynesian Revolution, Classical-Sraffian counter-revolution and the rise of Game Theory. By the 1980s, the first three had been "beaten back" by the Neoclassicals with different degrees of success; Game Theory, however, has proven to be a far more resilient beast and might conceivably yet undo considerable parts of Neoclassical theory, and perhaps the Marginalist Revolution as a whole, in the future.